A093357 Number of occurrences of pattern 2-1 after n iterations of morphism A007413.

0, 4, 20, 88, 368, 1504, 6080, 24448, 98048, 392704, 1571840, 6289408, 25161728, 100655104, 402636800, 1610579968, 6442385408, 25769672704, 103078952960, 412316336128, 1649266393088, 6597067669504, 26388274872320

Offset: 1

Author

Ralf Stephan, Apr 27 2004

Keywords

• nonn
• easy

Links

• S. Kitaev and T. Mansour, Counting the occurrences of generalized patterns....
• Index entries for linear recurrences with constant coefficients, signature (6, -8).

Crossrefs

Cf. A007413, A010036.

Programs

Mathematica

Join[{0},Table[(3*4^(n-1)-2^n)/2,{n,2,30}]] (* or *) Join[{0}, LinearRecurrence[{6,-8},{4,20},30]] (* Harvey P. Dale, Apr 04 2012 *)

PARI

a(n)=if(n==1,0,(3*4^(n-1)-2^n)/2)

Formula

a(1) = 0, a(n) = (3*4^(n-1) - 2^n)/2.

G.f.: 4*x*(1-x)/((1-2*x)*(1-4*x)).

a(1)=0, a(2)=4, a(3)=20, a(n)=6*a(n-1)-8*a(n-2). - Harvey P. Dale, Apr 04 2012

a(n) = 4*A010036(n-2). - R. J. Mathar, Apr 07 2022